Perhaps I worded my question poorly---let me rephrase it, using carbon for the example. Do you think that carbon was "born" as carbon, or was it a hydrogen atom that picked up a neutron (becoming deutrium), then went through fusion 5 times with 5 other deutrium atoms, thus becoming carbon. In other words, did all the elements start off as a hydrogen atom?

Yes - The protons and electrons ( and some neutrons) were all created in the big bang.
A proton and an electron together form a hydrogen atom.
Stars combine hydrogen atoms together by nuclear fussion to make helium, carbon, silicon etc all the way upto iron.
(The actual pathways of which elements are conbined to get which others in what order are fairly simple. see http://en.wikipedia.org/wiki/Proton-proton_chain and http://en.wikipedia.org/wiki/CNO_cycle)

To make anything heavier than iron you need the much higher energies of an exploding star - a supernova.